Related papers: Local-in-time Solvability and Space Analyticity fo…

For initial data $f$ in a subcritical Lorentz space $L^{p,q}(\mathbb{R}^{n}) \hookrightarrow \dot B^{-\frac np}_{\infty,\infty}(\mathbb{R}^n)$ ($n<p<\infty$, $1\leq q \leq \infty$), we prove results which imply in particular that a local in…

In this paper, we simplify and extend the results of \cite{GZ} to include the case in which $\Om =\R^3$. Let ${[L^2({\mathbb{R}}^3)]^3}$ be the Hilbert space of square integrable functions on ${\mathbb {R}}^3 $ and let ${\mathbb…

In this paper, we are concerned with the local-in-time well-posedness of a fluid-kinetic model in which the BGK model with density dependent collision frequency is coupled with the inhomogeneous Navier-Stokes equation through drag forces.…

In this paper, we study the initial and boundary value problem of the Navier-Stokes equations in the half space. We prove the unique existence of weak solution $u\in L^q(\R_+\times (0,T))$ with $\nabla u\in L^{\frac{q}{2}}_{loc}(\R_+\times…

In this paper, we consider the three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity in presence of vacuum over bounded domains. Global-in-time unique strong solution is proved to exist when $\|\nabla…

We prove the time analyticity for weak solutions of inhomogeneous parabolic equations with measurable coefficients in the half space with either the Dirichlet boundary condition or the conormal boundary condition under the assumption that…

We consider the two dimensional Navier-Stokes equations in vorticity form with a stochastic forcing term given by a gaussian noise, white in time and coloured in space. First, we prove existence and uniqueness of a weak (in the Walsh sense)…

We consider the Cauchy problem for the incompressible Navier-Stokes equations in dimension three and construct initial data in the critical space $BMO^{-1}$ from which there exist two distinct global solutions, both smooth for all $t>0$.…

In this paper, we prove some results on the existence and decay properties of high order derivatives in time and space variables for local and global solutions of the Cauchy problem for the Navier-Stokes equations in Bessel-potential…

Let $u=(u_h,u_3)$ be a smooth solution of the 3-D Navier-Stokes equations in $\R^3\times [0,T)$. It was proved that if $u_3\in L^{\infty}(0,T;\dot{B}^{-1+3/p}_{p,q}(\R^3))$ for $3<p,q<\infty$ and $u_h\in L^{\infty}(0,T; BMO^{-1}(\R^3))$…

In this work we establish the formation of singularities of classical solutions with finite energy of the forced fractional Navier Stokes equations where the dissipative term is given by $|\nabla|^{\alpha}$ for any $\alpha\in [0, \alpha_0)$…

The long-time behavior of solutions of the three-dimensional Navier--Stokes equations in a periodic domain is studied. The time-dependent body force decays, as time $t$ tends to infinity, in a coherent manner. In fact, it is assumed to have…

For the initial boundary value problem of compressible barotropic Navier-Stokes equations in one-dimensional bounded domains with general density-dependent viscosity and large external force, we prove that there exists a unique global…

Exponential stabilization to time-dependent trajectories for the incompressible Navier-Stokes equations is achieved with explicit feedback controls. The fluid is contained in two-dimensional spatial domains and the control force is, at each…

This paper is devoted to the global solvability of the Navier-Stokes system with fractional Laplacian $(-\Delta)^{\alpha}$ in $\mathbb{R}^{n}$ for $n\geq2$, where the convective term has the form $(|u|^{m-1}u)\cdot\nabla u$ for $m\geq1$. By…

We analyze the forced incompressible stationary Navier-Stokes flow in $\mathbb{R}^n_+$, $n>2$. Existence of a unique solution satisfying a global integrabilty property measured in a scale of tent spaces is established for small data in…

This paper provides primarily an analytical ad hoc -solution for 3-dimensional, incompressible Navier-Stokes equations with a suitable external force field. The solution turns out to be smooth and integrable on the whole space. There is…

We consider the local well-posedness of strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with density containing vacuum initially. We first prove the local existence and uniqueness of…

We study the existence of a strong solution to the initial value problem for the incompressible Navier-Stokes equations in the whole space. Our investigation shows that a ``suitable'' weak solution to the problem becomes a strong one…

We consider the compressible Navier-Stokes system on time-dependent domains with prescribed motion of the boundary. For both the no-slip boundary conditions as well as slip boundary conditions we prove local-in-time existence of strong…